The profile of a decorative aluminum bracket is defined by the region RRR bounded by the vertical lines x=0x = 0x=0, x=10x = 10x=10, the xxx-axis, and the curve
y=15x+1 y = 15\sqrt{x + 1} y=15x+1All dimensions are given in centimetres.
By using a single trapezium extending across the full width of the region, calculate an approximation for the area of RRR. Provide your answer in cm2\text{cm}^2cm2 to two decimal places.
A set of 3 identical aluminum brackets is manufactured to this specification. Each bracket is cut from a sheet with a uniform thickness of 6 mm6\text{ mm}6 mm and the density of the aluminum used is 2.7 g/cm32.7\text{ g/cm}^32.7 g/cm3.
Use the trapezium rule with six ordinates (utilising the boundaries and four equally spaced internal points) to estimate the total mass of the 3 brackets combined. Give your answer to the nearest gram.
Without further calculation, state why the mass determined in part (b) could be: (i) an underestimate, (ii) an overestimate.